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Surface terms as counterterms in the AdS-CFT correspondence
Open accessAbstract
We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti--de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions $d<~7.$ As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.
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“Traditionally this accomplished either by the method of background subtraction, or, in the case of asymptotically AdS spacetimes including a local counterterm action [18,345].”
From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [18]
In the citing paper
“In holography the leading result for the partition function, valid at large central charge, which we denote generically by c , is given by an appropriately regularized version of the on-shell action of the Euclidean black hole or whichever other classical saddle dominates in the bulk, [55]”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [55]
In the citing paper
“As in holographic renormalization [17][18][19][20][21], a tower of higher-derivative corrections to the d-dimensional Einstein-Hilbert action are induced by the holographic cutoff CFT d .”
From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [18]
In the citing paper
“These divergences may be removed via holographic renormalization, a prescription that adds appropriate local counterterms [17][18][19][20][21] in a minimal subtraction scheme.”
From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [18]
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Metadata
- Authors
- Emparan, R., Johnson, C. V., & Myers, R. C.
- Affiliations
- University of the Basque Country (ES)
- University of Kentucky (US)
- McGill University (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1999-10-01
- Volume
- 60
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2137060839
- Cited by
- 703
- References
- 49
- Citations by year
- 2026: 19 · 2025: 27 · 2024: 31 · 2023: 48 · 2022: 30 · 2021: 46 · 2020: 37 · 2019: 33 · 2018: 24 · 2017: 27 · 2016: 26 · 2015: 12 · 2014: 31 · 2013: 17 · 2012: 32
- FWCI
- 21.23
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Dipòsit Digital de la Universitat de Barcelona (Universitat de Barcelona) (publishedVersion)
- RECERCAT (Consorci de Serveis Universitaris de Catalunya) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Hispana (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9733173)
- Natural Sciences and Engineering Research Council of Canada
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- AdS/CFT correspondence, counterterms, boundary counterterms, asymptotically AdS spacetimes, topological black holes, background subtraction, finite action, vanishing cosmological constant, asymptotically flat spacetimes, holography
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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